Statics: a hinge held up by a string with a mass

[bfusco]

Homework Statement

A uniform beam of mass M and length L is mounted on a hinge at a wall as shown in the figure. It is held in a horizontal position by a wire making an angle (theta) as shown. A mass m is placed on the beam a distance from the wall, and this distance can be varied.

http://session.masteringphysics.com/problemAsset/1058226/6/GIANCOLI.ch12.p84.jpg

a)Determine, as a function of x, the tension in the wire.
Express your answer in terms of the variables m, M, L, x, θ, and appropriate constants.

b)Determine, as a function of x, the horizontal component of the force exerted by the hinge on the beam. Assume that the positive x and y axes are directed to the right and upward, respectively.

c)Determine, as a function of x, the vertical component of the force exerted by the hinge on the beam.

The Attempt at a Solution

a)first i realized that the force from the hinge and force due to tension had components.

choosing the hinge for the torque axis of rotation, i used the equation ƩFx=0, Fhx-Tx=0, Fhx=Tx. Then i used ƩFy=0, Fhy+Ty-mg-Mg=0 (here i didn't know what to solve for) and finally i used the equation Ʃτ=0, LT-xmg-(L/2)Mg=0, T=(xmg+(L/2)Mg)/L and it is at this point i don't see how i have yet to solve for anything useful to simplify any of the other equations.

 

[tal444]

I'm not sure why you would need to solve for anything. Isn't the question simply asking for an equation involving those variables?

 

[azizlwl]

Torque=F.r.Sinθ

 

[bfusco]

I'm not sure why you would need to solve for anything. Isn't the question simply asking for an equation involving those variables?

yes, but I am focusing on solving for the force due to tension (FT). so i somehow need to work the equations to solve for FT while taking the Fh (force from the hinge) out of the equation. With the Fh in the equation there are 2 unknown variables and that wouldn't be a function of x.

 

[tal444]

I'm confused, ignore the hinge for the moment if it's your axis. Your equation should be something like the (force of center of gravity)(length acting on) + (force of mass)(length acting on) = (tension on cable)(length acting on). Rearranging that equation, I see no Fh that you speak of.